Elsevier

Procedia Computer Science

Volume 29, 2014, Pages 1870-1875
Procedia Computer Science

A One-step Steffensen-type Method with Super-cubic Convergence for Solving Nonlinear Equations1

https://doi.org/10.1016/j.procs.2014.05.171Get rights and content
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Abstract

In this paper, a one-step Steffensen-type method of order 3.383 is designed and proved for solving nonlinear equations. This super-cubic convergence is obtained by self-accelerating second-order Steffensen's method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Numerical examples confirm the theoretical results and high computational efficiency.

Keywords

Nonlinear equation
Newton's method
Steffensen's method
Derivative free
Self-accelerating

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Selection and peer-review under responsibility of the Scientific Programme Committee of ICCS 2014.

1

Supported by Beijing Natural Science Foundation (No.1122014).